SEAMO 2027 - Paper E - SET 04 - Self-study Question 8

In triangle $ABC$, $\angle A=30^\circ$, $\angle C=90^\circ$ and $AC=1$. Outside $ABC$, draw equilateral triangles $BCP$, $CAQ$ and $ABR$. Let $QR$ meet $AB$ at $T$. Find the area of triangle $PQT$.